Question 1200431
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Start facing directly north.
Then turn 60 degrees toward the east (i.e. to the right).
This will align you with the bearing 060°
This is in the northeast quadrant.


Compass Rose:
<img src = "https://upload.wikimedia.org/wikipedia/commons/e/e9/Compass_rose.png">
Image courtesy of Wikipedia.
https://en.wikipedia.org/wiki/File:Compass_rose.png


This is what your rough sketch of the diagram should look like
{{{
drawing(400,400,-5,5,-5,5,
line(-1,2,-1,-2),
line(-1,-2,3,-2),
line(-1,-2,2,1),

locate(-1,-2,"P"),
locate(2,1,"Q"),

locate(-0.8,-0.46,60^o),
locate(0.14,-1.32,30^o),
locate(0.66,0.2,"8"),
locate(-5,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}
The boy starts at point P and moves to point Q.
Note that 60+30 = 90.


Let's erase the vertical line and erase the "60 degree" label.
I'll add in a vertical line from Q to drop down to the horizontal line.
It has length x to represent how far north Q is compared to P.
{{{
drawing(400,400,-5,5,-5,5,
line(-1,-2,2,-2),
line(-1,-2,2,1),
line(2,1,2,-2),

line(1.7,-2,1.7,-1.7),
line(1.7,-1.7,2,-1.7),

locate(-1,-2,"P"),
locate(2+0.1,1+0.3,"Q"),
locate(2,-2,"R"),
locate(2+0.2,-0.5,"x"),

locate(0.14-0.5,-1.32,30^o),
locate(0.66-0.5,0.2-0.5,"8"),
locate(-5,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}
The goal is to have a right triangle, so we can use a trig ratio to determine x.


sin(angle) = opposite/hypotenuse
sin(30) = x/8
x = 8*sin(30)
x = 8*0.5
x = 4
This value is exact. 
Make sure your calculator is in degree mode.


Answer: <font color=red>4 km</font>
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